1. **State the problem:** Simplify the expression $$\left( \frac{5x^{13} y^5 z^2}{3 \cdot 5^2} \right)^0$$. 2. **Recall the zero exponent rule:** Any nonzero expression raised to the power of zero equals 1, i.e., $$a^0 = 1$$ for $$a \neq 0$$. 3. **Apply the rule:** Since the entire fraction is raised to the zero power, regardless of the numerator or denominator (as long as it is not zero), the expression simplifies to: $$\left( \frac{5x^{13} y^5 z^2}{3 \cdot 5^2} \right)^0 = 1$$. 4. **Final answer:** $$1$$